Ultrafast magnetization enhancement via the dynamic spin-filter effect of type-II Weyl nodes in a kagome ferromagnet

The magnetic type-II Weyl semimetal (MWSM) Co3Sn2S2 has recently been found to host a variety of remarkable phenomena including surface Fermi-arcs, giant anomalous Hall effect, and negative flat band magnetism. However, the dynamic magnetic properties remain relatively unexplored. Here, we investigate the ultrafast spin dynamics of Co3Sn2S2 crystal using time-resolved magneto-optical Kerr effect and reflectivity spectroscopies. We observe a transient magnetization behavior, consisting of spin-flipping dominated fast demagnetization, slow demagnetization due to overall half-metallic electronic structures, and an unexpected ultrafast magnetization enhancement lasting hundreds of picoseconds upon femtosecond laser excitation. By combining temperature-, pump fluence-, and pump polarization-dependent measurements, we unambiguously demonstrate the correlation between the ultrafast magnetization enhancement and the Weyl nodes. Our theoretical modelling suggests that the excited electrons are spin-polarized when relaxing, leading to the enhanced spin-up density of states near the Fermi level and the consequently unusual magnetization enhancement. Our results reveal the unique role of the Weyl properties of Co3Sn2S2 in femtosecond laser-induced spin dynamics.


Supplementary Note 1. Origin of the initial peak in time-resolved magneto-optic Kerr rotation
To investigate the origin of the initial peak in the TR-MOKE results around zero delay, we firstly consider the contribution of the specular inverse Faraday effect (SIFE) and specular optical Kerr effect (SOKE).These coherent third-order effects only occur during the period of pump excitation.Interestingly, as shown in Supplementary Fig. 6c, the rising edge of the initial peaks from TR-MOKE and TR-R coincide perfectly.This indicates that the initial peak is determined by the state occupation upon pump excitation.In Supplementary Fig. 6d, the amplitude of the initial peak from TR-MOKE as a function of temperature is plotted (from the fitting results in Fig. 2 in the main text).Overall, the amplitude decreases with increasing temperature and completely vanishes when the temperature reaches the Curie temperature.It is noted that the observed peak around 130 K corresponds to the peak observed in the ZFC curve in Fig. 1h and in Ref. 3.Although the underlying mechanism of this anomalous magnetic transition is still unclear, the amplitude of the initial peak from time-resolved Kerr rotation is highly dependent on the macroscopic magnetization.Thus, the initial peak from time-resolved Kerr rotation can be attributed to the so-called dichroic bleaching or state blocking effect 4,5 .This effect can be interpreted as a breakdown of the proportionality between the magnetization and the Voigt vector that is the basis of magneto-optics due to the consequence of the out-ofequilibrium character of the electron system immediately after the femtosecond excitation.To verify the bleaching and state-blocking effect, a spectral dependence in the magneto-optical response would be expected 6 .Unfortunately, although the spectral dependence of the magneto-optical effect in Co3Sn2S2 has been studied recently, the photon energy used was very low (terahertz to 1 eV) 7 .The spectral dependence of the magneto-optical response around the wavelength of the probe pulse (400 nm) still deserves further investigation.Nevertheless, as this bleaching or state-blocking effect only lasts during the first hundreds of femtoseconds upon pump excitation, the subsequent magneto-optical response predominantly reflect the genuine spin dynamics in Co3Sn2S2.

Supplementary Note 2. Details of data fitting process
We carefully fitted our experimental results, and extensive effort has been made to avoid any artifact or over-interpretation during the fitting process.As discussed in the main text, numerically fitting three competing magnetization dynamic processes (and the initial peak) is difficult because each component has a characteristic enhancement (demagnetization) time and a corresponding relaxation time.If we fit all these three pairs of time constants as free variables, the fitting results could be divergent and arbitrary.Therefore, we fixed several parameters correspondingly when processing the pump fluence-dependent results at 10 K.
For the TR-MOKE curves measured at 10 K with various pump fluences, we found that all the curves can be fitted very well with a fixed combination of  ℎ = 2 ps,   = 300 fs and   = 6 ps.In Ref.The fitting values of all the parameters for the pump fluence-dependent at 10 K and temperature-dependent at 0.57 mJ/cm 2 measurements are included in Supplementary Table 2 and 3, respectively.

Supplementary Note 3. Potential mechanisms for the ultrafast magnetization enhancement
Ultrafast laser-stimulated magnetization enhancement on a 100 ps timescale was observed in the diluted magnetic semiconductor GaMnAs 10 .This photoenhanced ferromagnetism was attributed to the collective ordering to the p-d exchange interaction between photoexcited holes and Mn spins.Two key pieces of evidence for this Mn-hole correlation are the experimentally observations of the peak near 20 K of the photoenhanced ferromagnetism and the observed enhanced magnetization even above the Curie temperature.However, in Co3Sn2S2, the magnetization enhancement is monotonously decreasing with increasing temperature.Also, no transient Kerr rotation is observed in Co3Sn2S2 when the temperature is higher than the Curie temperature, regardless of the pump fluence.Therefore, this nonthermal 3d transition metal-hole exchange correlation-induced magnetization is not the mechanism responsible for our results.
It has been reported that ultrafast photoinduced insulator-metal transitions can induce ultrafast antiferromagnet-ferromagnet transitions in perovskite-type Gd0.55Sr0.45MnO3 11.Firstly, the photocarriers melt the charge-ordered and orbit-ordered insulator phase, and the metallic state is formed within the time resolution of ~200 fs.
Meanwhile, the charge excitation destructs the charge ordering and causes the charges to become delocalized.Secondly, in the delocalized state, the manipulated doubleexchange interaction causes the spins to align ferromagnetically.In Co3Sn2S2, although theoretical investigations indicate that the third-neighbor exchange coupling via Co-Sn-Co dominates when temperature is below the Weyl nodes annihilation temperature 12 , this switched-on exchange-based ultrafast magnetization enhancement is extremely fast with a characteristic time of 20 fs for Gd0.55Sr0.45MnO3(corresponding to the double exchange energy of ~0.2 eV).The calculated effective energy of the third-neighbor exchange in Co3Sn2S2 is ~0.03 eV 12 , which corresponds to a characteristic time of ~133 fs.However, the characteristic time of our observed magnetization enhancement is ~2 ps, which is larger than 133 fs by an order of magnitude.Also, this exchange-couplinginduced magnetization enhancement cannot lasts for a long time (decay in ~10 ps for Gd0.55Sr0.45MnO3),while the magnetization enhancement in Co3Sn2S2 shows a long relaxation time of over 100 ps.From a microscopic view, unlike the insulating Gd0.55Sr0.45MnO3,Co3Sn2S2 is a semimetal that does not exhibit (weak) charge ordering.
Thus, the laser pulse cannot stimulate the destruction of charge ordering and subsequently tuning of the exchange coupling.Therefore, the observation of magnetization enhancement in Co3Sn2S2 cannot be attributed to photoinduced (charge delocalized) exchange coupling modulation, although the exact evolution of exchange coupling upon the laser stimulation is worth further investigation.
Ultrafast magnetization enhancement was also observed in metallic multilayers driven by superdiffusive spin current 13 .However, this effect can be safely excluded in our experiments as there is no adjacent magnetic compound.
process due to intrinsic half-metallic nature.The Elliot-Yafet spin-flip provides an interaction channel between the electron and spin systems via the band mixing for majority and minority spins.Instead of this direct angular momentum transfer, in halfmetals the spin-lattice interaction plays an overwhelming role which is mediated by spin-orbit coupling 17,20 and the time constant of this spin thermalization process is much longer than the normal demagnetization time in transition metals.measurements support our analysis of the initial peak in the manuscript.We note that ellipticity measurements may provide more information about the initial peak, which certainly deserve further study in future work.S2.Fitting parameters for the pump fluence dependent measurements when temperature is 10 K.

Supplementary Figure 2 |Supplementary Figure 6 |
Measured transient Kerr signal and reflectivity change under opposite applied magnetic fields.a, The measured Kerr signal under opposite applied magnetic fields ∆  (, ) (black curve) and ∆  (, −) (red curve).The transient Kerr rotation change ∆  () is defined in the following as the asymmetric part, changing with the field direction ∆  () = (∆  (, ) − ∆  (, −)) 2 ⁄ .b, The measured reflectivity change under opposite applied magnetic fields show no difference.The pump fluence is 1.13 mJ/cm 2 .Supplementary Figure 3 | Hall data of Co3Sn2S2 crystal.a, Hall resistivity  xy A measured at different temperatures.b, Temperature dependence of the anomalous Hall conductivity  xy A at zero magnetic field.c, Temperature dependence of the anomalous Hall resistivity  xy A .The peak around 150 K is consistent with the observation in ref. 3 .d, Temperature dependence of the longitudinal resistivity  xx at zero magnetic field.e, Temperature dependence of the anomalous Hall angle  xy A  xx ⁄ at zero magnetic field.f, The anomalous Hall conductivity  xy A as a function of the longitudinal charge conductivity  xx .Analysis of the initial peak in measured time-resolved magneto-optic Kerr rotation.a, The measured transient MOKE signal change with different combinations of the applied magnetic field direction (positive H + and negative H − ) and the pump helicity (left handed σ + and right handed σ − ).b, The differential TR-MOKE curves with respect to the pump helicity under the same direction of the applied magnetic field (blue and black) and the transient Kerr rotation curve (red).c, The transient Kerr rotation (red) and the transient reflectivity change (black).d, The amplitude of the initial peak from time-resolved Kerr rotation A4 as a function of temperature e, FWHM of the initial peak from time-resolved Kerr rotation.
8,9, by applying the time-resolved angularresolved photoemission spectroscopy (TR-ARPES), which is surface sensitive, a critical behavior of the demagnetization time is observed with respect to the pump fluence in Ni film.Two unchanged values of the demagnetization time are observed below or above the critical pump fluence.Therefore, the demagnetization dynamics observed by TR-MOKE with a continuously varied demagnetization time as a function of the pump fluence can be interpreted as an integration of the magnetic response over the penetration depth of the probe light.From the sample surface the pump fluence is attenuated gradually within the penetration depth.Here, in this study, the three magnetization dynamic components can be qualitatively distinguished in Fig.1k.Although whether (part of) these components observed in Co3Sn2S2 have a critical behavior with respect to the pump fluence as similar as Ni is unknown, we believe the current fitting method to recognize each magnetization dynamic components is scientifically sound.Indeed, the precise values of the demagnetization (enhancement) time constant and their pump fluence dependence are desirable (and call for the further investigation).However, the three distinct characteristic time constants  ℎ = 2 ps,   = 300 fs and   = 6 ps can sufficiently provide information for the following discussion.For the TR-MOKE curves measured as a function of temperature, as shown in Fig.2a, the assumption of unchanged characteristic times for each magnetization dynamic component is not reasonable because temperature variation would affect both the macroscopic magnetization and the topological properties.In this case, we choose the temperature-dependent TR-MOKE results with a low pump fluence of 0.57 mJ/cm 2 for investigate.As shown in Supplementary Fig.7, the TR-MOKE curves measured at 10 K show that the A3 component (slow demagnetization) is considerably small compared to the other two components under such low pump fluence.Thus, we ignore the A3 component when fitting the temperature dependent TR-MOKE curves when the temperature is lower than 90 K.All the other parameters, including  ℎ ,   and   , are open for fitting.We note that the A3 amplitude below 90 K as shown in Fig.2cshould be a very small value rather than absolute zero.However, this simplification does not affect the key observation of the transition around 110 K.The fitted values of  ℎ and   , as shown in Supplementary Table .
3, are close to the values used in the pump fluence-dependent results at 10 K, which demonstrates again the validity of the fitting method mentioned above.
Field cool measurements on temperature dependence of magnetization, the applied filed is 1 Tesla along c axis.
The transient MOKE change with different combinations of the applied magnetic field direction (positive H + and negative H − ) and the pump helicity (left handed σ + and right handed σ −) is shown in Supplementary Fig.6a.The pump helicity-induced effect dominates around zero delay can be clearly distinguished, disappearing within 0.5 ps.The differential TR-MOKE curves with respect to the pump helicity under the same